Everyone who has some experience with mathematics might be familiar with encountering impasses and feeling confused when solving challenging mathematical problems. The literature has shown that impasses are related to epistemic emotions (i.e. surprise, curiosity, confusion) and learning processes among adults. But, there is limited research on the relations between these three factors in younger populations. Let’s see how Munzer et al. (2021) investigated this issue.

To fill the gap, Munzar et al. (2021) proposed a theoretical model of the relations between cognitive factors (e.g. control, value, cognitive disequilibrium), affective factors (e.g. surprise, curiosity, confusion, frustration), and self-regulated learning processes during mathematical problem-solving. They conducted two studies to test their model. In the first study, 136 elementary students from Grade 3 to 6 reported their value and perceived control for learning mathematics and solving mathematical problems on the first day. On the second day, students were asked to solve a mathematical problem and talk out-loud about everything that they were thinking and doing during problem-solving. Students’ epistemic emotions were assessed after the problem-solving activity. Results showed that students who showed higher levels of perceived control were less likely to encounter impasses when solving challenging mathematical problems. Moreover, students’ cognitive disequilibrium, which refers to “a state of uncertainty and disorientation when there is a mismatch between incoming information and existing mental models” and is signaled by impasses, positively predicted their epistemic emotions such as surprise, confusion, and frustration. It is worth noting that when an impasse was unexpected, students experienced surprise before curiosity and confusion.

In the second study, the researchers aimed to explore reciprocal effects between students’ epistemic emotions following impasses and their cognitive appraisals of perceived control and value for learning mathematics and solving mathematical problems as they work on challenging problems. 80 fifth graders solved a difficult mathematical problem over two days. Their perceived control and value were assessed both before they started solving the problem and after most of the students had finished problem-solving. Self-reported emotions were collected at the end of each session. Results indicated that curiosity following successful resolution of impasses predicted students’ perceived control after completing the task. However, confusion following unsuccessful resolution of the impasse predicted frustration and help-seeking behaviors. Such confusion and frustration predicted decreased perceived control after task completion if the impasse remained to be unresolved.

Despite all of these findings, one of the most important results is the fluid nature of students’ perceived control for learning mathematics and solving mathematical problems. The emotions experienced by students during problem-solving served as feedback for them to adjust their perceptions of control accordingly. In accordance with EPIC’s goal of helping learners to maximize the benefits of failures, Munzer et al.'s (2021) study sheds light on the importance of teaching students how to interpret confusion and frustration in a way that enhances rather than discourages perceptions of control during learning. The study also supports the need for future educational interventions to support students in challenging learning experiences. For instance, educators can emphasize the universality of experiencing confusion and frustration when solving challenging problems. Moreover, educators can foster students’ awareness of help-seeking when they are too confused to move forward independently. Educators can also carefully monitor students’ progress through a learning task and provide learners with appropriate tools and strategies to help them resolve impasses. 

For more information about Munzar et al.’s (2021) study, check out the link below for the article:

https://psycnet-apa-org.tc.idm.oclc.org/doi/10.1037/edu0000460

Reference:

Munzar, B., Muis, K. R., Denton, C. A., & Losenno, K. (2021). Elementary students’ cognitive and affective responses to impasses during mathematics problem solving. Journal of Educational Psychology, 113(1), 104–124. https://doi-org.tc.idm.oclc.org/10.1037/edu0000460